Antigoni Kaliontzopoulou, CIBIO/InBIO, University of Porto
12 October, 2019
Different types of asymmetry are thought to have a biological meaning
Directional asymmetry: consistent difference skewed towards one of the sides (at the population level); thought to reflect difference in use, e.g. fiddler crabs feeding vs. fighting displays
\[\small{SST}=\sum^n_1{D}^2_{(X_i,Y_i)}=nD^2_{(\overline{X},\overline{Y})}+\sum^n_1{D}^2_{(X_i-\overline{X},Y_i-\overline{Y})}\]
One can approach the problem by defining Symmetry Groups
Symmetry groups: transformations that leave the data invariant
e.g.: bilateral symmetry = reflection across the midline
Symmetry groups define transformations such that there are invariances in those symmetric ‘dimensions’
These groups describe the ways in which symmetry can be defined, and thus quantified for more complex structures (e.g., radial symmetry)
For articulated structures, several solutions exist - Fixing the angle in all specimens through a mathematical transformation - Separating the subsets to analyse separately, etc.